If U = R and A = {x ∈ R : x ≥ 3}, what is Aᶜ?
Answer and explanation
Correct answer: {x ∈ R : x < 3}
The set A contains 3 and every real number greater than 3, so A = [3, ∞). The complement is taken with respect to the universal set R, meaning we select all real numbers not belonging to A. These are precisely the real numbers less than 3. The endpoint 3 is excluded because 3 belongs to A. Therefore Aᶜ = {x ∈ R : x < 3}, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
{x ∈ R : x < 3}
Why is this the correct answer?
The set A contains 3 and every real number greater than 3, so A = [3, ∞). The complement is taken with respect to the universal set R, meaning we select all real numbers not belonging to A. These are precisely the real numbers less than 3. The endpoint 3 is excluded because 3 belongs to A. Therefore Aᶜ = {x ∈ R : x < 3}, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
